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"For me, it was a no-brainer," Cole said on Derby's YouTube channel. "Of course, I've kept in touch with Lamps [Lampard], to see how good the team has been playing and followed Derby since Lamps got here.

"For me, it was a no-brainer to come here and get involved in this great environment and hopefully push for promotion."

Cole, 38, started his career at Arsenal where he won two league titles and three FA Cup medals before joining Chelsea in 2006. At Stamford Bridge, he won another Premier League title as well as a Champions League and Europa League.

He also enjoyed four more FA Cup victories, which made him the most successful player in the competition's history with seven.

In 2014, he joined Roma before moving onto LA Galaxy in Major League Soccer after two seasons in which he made 11 Serie A appearances.

Cole played alongside Lampard for eight seasons at Chelsea while, John Terry, who captained the pair at Stamford Bridge, is also competing for promotion from the Championship as Aston Villa assistant manager.

Cole retired from international football in 2014 with 107 caps, which made him England's most capped full-back.